 Hi, this is Dr. Don. I have a problem out of Chapter 8 where we're dealing with the difference in two population proportions. In this problem, we're told that we have a study about the effectiveness of using magnetic insoles to treat a form of heel pain, and it tells us that 53 subjects wore the insoles. 48 did not wear the magnetic insoles. We're given an alpha, and we want to answer the question, can you support the claim that there is a difference in the proportion of subjects who felt better? We assume the random samples are independent. When we look at this information, one thing that should jump out to you given these pie charts, that we're dealing with two categorical variables, which we have counts. And when we're given counts and a categorical variables, those are proportions, all proportion hypothesis tests that we run use the z-test. First thing we have to do is identify the null and alternative. Here it says, can you support the claim there is a difference? If there's a difference, that means that the two proportions are not equal. So the proportions of the two groups are different. And if we look at the options there, we will find over here that proportion one equal portion two, and the claim is that the two proportions are not equal. The first thing we need to do is find the critical value, and we're going to use stat crunch to do that. Remember we can go up here to question help, click on the drop down box, and open up stat crunch. Okay, I have stat crunch open, and as usual we start with the stat button. We drop down to calculators because we're using the z-test, and that is the normal calculator. We have a not equal, which is a two-tail test, so I like to use the between calculator to do that. Our alpha is 0.07, which means that our confidence level is one minus alpha would be 0.93. And when we use the between calculator, we put that confidence level in here, 0.93, and click compute, and that gives us our chart showing the rejection regions. Now here the 0.93 is the confidence level area, so our rejection regions are these white areas on either end of the two-tail test, minus 1.81 and plus 1.81. And those are the answers they wanted in the problem. We scroll down here, and we've given the rejection region and the critical values. Now we need to get the standardized test statistic, z, and then make a decision and draw a conclusion. So we'll go back to stat crunch, and we go back to stat. This time we go not to z-stats. We've got a tool for proportion stats. We've got two samples, and we have a summary since we have the count. And we bring this up. Number successes in the feel better magnetic side was 17, and the total was 53. The feel better in the non-magnetic was 22, and the total was 48. We want to run the hypothesis test for the proportion difference. Here we're saying that it was 0. There is no difference as the null, the claim was the alternative, that the two proportions are different. We just click on compute, and we get our answer. You've got a rehash there of the counts, successes in totals, the test statistic, and then the standardized test statistic over here, 1.42 rounded, and a p-value of 0.15, which is bigger than the alpha 0.07, which means we fail to reject the null hypothesis. If we bring back up our chart here, we can see that this minus 1.42 falls over here somewhere, and that is not in the rejection area. So again, if we use the critical value approach to the hypothesis test, we get the same answer, fail to reject. So we go back over here to the final thing, and we've decided to fail to reject. The claim was the alternative, so our answer must be at the 7% significance level. We always need to give the significance level since if the significance level were different, we could get a different decision and different conclusion. But here there was insufficient evidence to support the claim because we did not reject the null. I hope this helps. And if it does help, please consider subscribing to my YouTube channel, Stats Files. Just click the big red subscribe button.